In the article I find myself agreeing more with Sherrilyn Roush than with Keith Simonton. Prior to Einstein and Planck, most scientists thought they had it ``all figured out'' - boy did that change in a short 20 years.
In my opinion (as a physicist) the ``big problem'' with scientific advancement right now is that pretty much the
only method we have to solve complex equations is
perturbation theory. It works ``reasonably'' well, and provides some useful results - but it has its limits.
Basically
all of the ``big problems'' in physics are subject to the caveat of perturbation theory.
General Relativity cannot be reconciled with Quantum Mechanics...
by perturbation theory alone (unlike, say, Electrodynamics and Quantum Mechanics).
Many astronomical phenomena like galactic rotations curves and some instances of gravitational lensing cannot be reconciled with General Relativity...
by a perturbative solution to the GR equations.
Big, fundamental problems with existing theoretical frameworks
may exist, but it is hard to find them since the best tool we have to work with these existing theoretical frameworks is perturbation theory, which has its
own set of well-known limitations.
Hopefully some math genius will pop up someday with a new method for avoiding the problems of perturbation theory... and then we will
definitely see a very productive decade (or two) of scientific advancement.